The prose is very lucid and easy to follow. References are given to websites as well as books.
#Basic number theory review update
The format of the book makes it especially easy to update as advances in the subjects occur, particularly computational advances. The content is very accurate ad up to date. There is a very good index and glossary and a good review of notation and basic facts in the first chapter. Reviewed by William McGovern, Professor, University of Washingon on 8/21/16Īs promised by the title, the book gives a very nice overview of a side range of topics in number theory and algebra (primarily the former, but with quite a bit of attention to the latter as well), with special emphasis to the areas in which computational techniques have proved useful. There do not appear to be major grammatical errors in the text.ĭue to the topics in this text, this question does not appear to be applicable.
#Basic number theory review pdf
There do not appear to be any problems with the interface of the PDF of the text. For this reason, an instructor may want to choose certain sections in a chapter to cover as prerequisites for an application, instead of covering the material linearly. The book jumps from chapters on purely algebraic topics to those focused on applications. Depending on a course's focus, this could be done fairly easily.Įach chapter is written in a logical manner, referencing previous material as needed. However, even among the remaining sections, an instructor would need to carefully choose sections that include all necessary prerequisite material. There are a few sections indicated that are not required for future material. Since the book is quite long, an instructor for a one-semester course would need to choose specific topics from the text to cover. The book's terminology and mathematical frameworks appear to be consistent. We should also point out that mathematical induction is a prerequisite for this text, and some of the material is presented using pseudocode, which is different than many texts on these topics. An instructor may want students to become comfortable with these topics initially through computations, using the Euclidean Algorithm. The Euclidean Algorithm is presented after sections on solving linear congruences modulo n, and the Chinese Remainder Theorem applications of the Euclidean Algorithm to these topics are presented later. Some sections are terse, and an instructor may want to supplement the theoretical exercises with some more computational ones. The presentation of topics is accurate, and starts "from scratch." All material necessary in future sections is included in the appropriate section. The book appears to be up-to-date, and includes some interesting applications of theoretical material to topics relevant in cryptography (e.g., the RSA cryptosystem, and primality testing). The author has a list of errata on his webpage. The text includes an effective index.įrom my research in writing this review, I have not come across any major errors. The Table of Contents indicates a few sections that are not required for future material. This, and other topics, are tools for interesting computational applications.
The book also includes an introduction to probability. The book starts with basic properties of integers (e.g., divisibility, unique factorization), and touches on topics in elementary number theory (e.g., arithmetic modulo n, the distribution of primes, discrete logarithms, primality testing, quadratic reciprocity) and abstract algebra (e.g., groups, rings, ideals, modules, fields and vector spaces, some linear algebra, polynomial rings and their quotients). This text is an introduction to number theory and abstract algebra based on its presentation, it appears appropriate for students coming from computer science. Reviewed by Emily Witt, Assistant Professor, University of Kansas on 8/21/16